Short answer is frame size is always important, just not as super-critical for us casual riders. Get the better bike, that is more comfortable when you test ride it. Rough estimate is maybe 1 to 2 inches between your jewels and the top tube. Then also make sure that your torso is at a comfortable angle and you are not leaning on the bars. My guess would be 21 inch.

FB4K - This December, 2014, 5288 kids received bikes for Christmas. For many, it was their first bike, ever. Every bike, new and used, was donated, built, cleaned and repaired. That amounts to well over 10,000 volunteer hours this fall, just in the Twin Cities. Check us out on FaceBook: FB4K.
Disclaimer: 99% of what I know about cycling I learned on BF. That would make, ummm, 1% experience. And a lot of posts.

I'll disagree, especially mountain bikes. I can have a blast on a 17" mountain bike, and I'm 6ft. Smaller MTB bikes are very cool and easy to handle technically. Forget about top bar clearance, that's nonsense.

Ride it, and if you can climb with leverage without your knees being cramped by the distance to the bars - you're good.

I can ride a 52cm frame with the right stem and seatpost or I can ride a 60cm frame. Others might disagree but I don't find frame size critical as long as its within the range you can modify it to fit. 2 inches smaller on an mtb can be a good thing. You want a smaller frame for riding downhill.